DN to Reflectance
HONDA Kiyoshi
Contents
Definition of NDVI
 Radiance
 Reflectance
 How to Calculate Radiance from DN
 Irradiance

Definition of NDVI
 NIR  VR
NDVI 
 NIR  VR
 NIR : Reflectance at Near Infrared
VR : Reflectance at Visible Red
Reflectance


Ratio of Radiant Energy Reflected to Incident Energy
Radiant Energy = Integral of vertical components of
Radiance Measured ( by satellite to be scaled back
from DN )
L
L
 

G  s Es
  : SpectralReflectance
L : SpectralRadiance of theSurface W / m 2  sr  m
G : SpectralIrradianceW / m 2  m
Es : SpectralSolar Irradiance W / m 2  m
 s  cos( s ), s : Solar zenithangle
E
πL
θ
DN ?
DN ( Digital Number ) you can see in
the RS image files is not Reflectance.
 So you have to derive Reflectance from
the DN
 Then what is DN ?

DN is a scaled Radiance

DN is scaled from Radiance measured
by sensors
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter6/chapter6.html
Radiance

Energy in unit time, unit
solid angle, unit wavelenth
Z
unit : J / s  m  sr  m  W / m  sr  m
2
Energy received
L 
dtdAd d
2
dλ
dω
dA
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter6/chapter6.html
QCALMAX
DN to Radiance (Lλ)
L  gain DN  offset
or
LMAX   LMIN
(QCAL  QCALMIN)  LMIN
L 
QCALMAX  QCALMIN
LMAX  LMIN
QCALMAX  QCALMIN
LMAX   LMIN
 LMIN
offset  
QCALMAX  QCALMIN
DN  QCAL, offset  bias
gain 

Have to find out LMAX,
LMIN, QCALMAX,
QCALMIN
QCALMIN
LMIN, LMAX of LANDSAT7

LMIN, LMAX List
LMAX
LMIN
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter11/chapter11.html
LANDSAT 7 Gain Setting for January
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter6/htmls/january_gains.html
How to Find the Constants for
Scaling factor of Radiance

Metadata file .met


Sample ftp://cgceopush3.geo.msu.edu/push3_2/137/043/p137r43_7x000228/p137r043_7x20000228.met
Identify Hi-Gain or Low Gain

EROS Data Center Gateway
• http://edcimswww.cr.usgs.gov/pub/imswelcome/

Obtain Hi-Gain and Low-Gain parameters

USGS LANDSAT Page
• http://landsat7.usgs.gov/technical_details/calibration_files/
Header file/record
 Data Handling Manuals


Processed in Japan, China, Thailand ….
How to obtain TOA Irradiance

Spectral Exo-atmospheric Irradiance
 
L
Es 
G

L
 s Es
ESUN
2
ds
Es : Exo - atmospheric Solar SpectralIrradiance W / m 2  m
ESUN : AverageExo - atmospheric Solor SpectralIrradianceW / m 2  m
d s : Earth- Sun distancein astronomical units
 s  cos( s ), s : Solar zenithangle
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter11/chapter11.html
Average Solar Spectral Irradiance ESUNλ

Average Solor Spectral
Exo-atmospheric
Irradiance
 
L
Es 
G

L
 s Es
ESUN
2
ds
Es : Exo - stomospheric Solar SpectralIrradiance W / m 2  m
ESUN : AverageExo - atmospheric SpectralIrradiance W / m 2  m
ESUNλ for ETM+
http://modarch.gsfc.nasa.gov/MODIS/ATM/solar.html
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter11/chapter11.html
Sun Earth Distance ds
Es 
1
ESUN
2
ds
d s : Earth- Sun distancein astronomical units
Relative Solar Irradiance 1/(ds*ds)
1.10
1.05
1.00
0.95
0.90
0
30
60
90
120
150
180
210
240
270
300
330
360
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter11/chapter11.html
Solar Zenith Angle

LANDSAT: Use Zenith Angle ( 90deg – Sun
Elevation) at the centre of the image for the
whole image


180km -> +- 0.81 deg
If Zenith Angle < 20deg, difference < 1%
Or

Calculate the angle from Lat, Lon, Julian day
and time ( i.e POSSOL of 6S ).
http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter11/chapter11.html
Atmospheric Correction




The reflectance we have obtained here is Apparent
Reflectance or Reflectance at TOA
Atmospheric correction is needed to obtain Reflectance at
Ground Level
You may run 6S with appropriate parameters
Some products are Reflectance at Ground Surface, such as
MODIS, SPOT VEGETAION…
References

Landsat 7 Science Data Users Handbook

Chapter6
•

Chapter 11
•

http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter11/chapter11.html
Dr. Kawamura's page DN->Refelctance for
Landsat ( Japanese )


http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter6/chapter6.html
http://www.geocities.jp/kensuke_kawamura/Others/LandsatCal
ibration/LandsatCalibration.html
6S Manual